In [1]:

import pathpyG as pp

import torch
from pathpyG.nn.dbgnn import DBGNN
from torch_geometric.transforms import RandomNodeSplit
import torch_geometric
from sklearn.manifold import TSNE
import numpy as np
import matplotlib.pyplot as plt
import scipy as sp

pp.config['torch']['device'] = 'cpu'
device = pp.config['torch']['device']

import pathpyG as pp import torch from pathpyG.nn.dbgnn import DBGNN from torch_geometric.transforms import RandomNodeSplit import torch_geometric from sklearn.manifold import TSNE import numpy as np import matplotlib.pyplot as plt import scipy as sp pp.config['torch']['device'] = 'cpu' device = pp.config['torch']['device']

Load the synthetic dataset¶

In [63]:

# Read temporal network
t = pp.TemporalGraph.from_csv('../data/temporal_clusters.tedges')

# Read temporal network t = pp.TemporalGraph.from_csv('../data/temporal_clusters.tedges')

In [3]:

node_colors = ['green']*10+['red']*10+['blue']*10

node_colors = ['green']*10+['red']*10+['blue']*10

In [4]:

style = {}
style['node_color'] = node_colors

style = {} style['node_color'] = node_colors

In [5]:

pp.plot(t, **style);

pp.plot(t, **style);

In [6]:

# read the paths
paths_original = pp.PathData.from_csv('../data/temporal_clusters.ngram')
print(paths_original)
print(paths_original.num_nodes)

# read the paths paths_original = pp.PathData.from_csv('../data/temporal_clusters.ngram') print(paths_original) print(paths_original.num_nodes)

PathData with 7460 walks and 0 dags and total weight 29042
30

In [7]:

#caluclate paths 
dag = pp.algorithms.temporal_graph_to_event_dag(t, delta=1)
print(dag)

#caluclate paths dag = pp.algorithms.temporal_graph_to_event_dag(t, delta=1) print(dag)

Graph with 89032 nodes and 60000 edges

Node attributes
	node_name		<class 'list'>
	node_id		<class 'list'>
	node_idx		<class 'list'>

Edge attributes
	edge_ts		<class 'torch.Tensor'> -> torch.Size([60000])

Graph attributes
	num_nodes		<class 'int'>

In [8]:

paths = pp.PathData.from_temporal_dag(dag)
paths.node_id = t.data.node_id
print(paths)

paths = pp.PathData.from_temporal_dag(dag) paths.node_id = t.data.node_id print(paths)

PathData with 29032 walks and 0 dags and total weight 29032

In [9]:

print(len(set([tuple(pp.PathData.walk_to_node_seq(v).tolist()) for v in paths.paths.values()])))

print(len(set([tuple(pp.PathData.walk_to_node_seq(v).tolist()) for v in paths.paths.values()])))

7078

In [10]:

# Create the graph corresponding to paths
g = pp.HigherOrderGraph(paths, order=1)

# Plotting the time-aggregated network (first-order graph)
pp.plot(g);

# Create the graph corresponding to paths g = pp.HigherOrderGraph(paths, order=1) # Plotting the time-aggregated network (first-order graph) pp.plot(g);

In [65]:

# Create the second-order graph corresponding to paths
g2 = pp.HigherOrderGraph(paths, order=2, node_id=t.data.node_id)

# Plotting the second-order graph
pp.plot(g2);

# Create the second-order graph corresponding to paths g2 = pp.HigherOrderGraph(paths, order=2, node_id=t.data.node_id) # Plotting the second-order graph pp.plot(g2);

In [12]:

t_shuffled = pp.TemporalGraph.from_csv('../data/temporal_clusters.tedges')
t_shuffled.data['t'] = t.data['t'][torch.randperm(len(t_shuffled.data['t']))]

t_shuffled = pp.TemporalGraph.from_csv('../data/temporal_clusters.tedges') t_shuffled.data['t'] = t.data['t'][torch.randperm(len(t_shuffled.data['t']))]

In [13]:

t.data.t

t.data.t

Out[13]:

tensor([    0,     1,     2,  ..., 59997, 59998, 59999])

In [14]:

t_shuffled.data.t

t_shuffled.data.t

Out[14]:

tensor([21541,  5967, 30001,  ...,  8319, 17186, 28812])

In [15]:

#caluclate paths 
dag_shuffled = pp.algorithms.temporal_graph_to_event_dag(t_shuffled, delta=1)
print(dag_shuffled)

#caluclate paths dag_shuffled = pp.algorithms.temporal_graph_to_event_dag(t_shuffled, delta=1) print(dag_shuffled)

Graph with 118015 nodes and 60000 edges

Node attributes
	node_name		<class 'list'>
	node_id		<class 'list'>
	node_idx		<class 'list'>

Edge attributes
	edge_ts		<class 'torch.Tensor'> -> torch.Size([60000])

Graph attributes
	num_nodes		<class 'int'>

In [16]:

paths_shuffled = pp.PathData.from_temporal_dag(dag_shuffled)
print(paths_shuffled)
print(paths_shuffled.num_nodes)

paths_shuffled = pp.PathData.from_temporal_dag(dag_shuffled) print(paths_shuffled) print(paths_shuffled.num_nodes)

PathData with 58015 walks and 0 dags and total weight 58015
30

In [66]:

# Create the second-order graph corresponding to paths
g2_shuffled = pp.HigherOrderGraph(paths_shuffled, order=2, node_id=t_shuffled.data.node_id)
print(g2_shuffled)

# Plotting the second-order graph
pp.plot(g2_shuffled);

# Create the second-order graph corresponding to paths g2_shuffled = pp.HigherOrderGraph(paths_shuffled, order=2, node_id=t_shuffled.data.node_id) print(g2_shuffled) # Plotting the second-order graph pp.plot(g2_shuffled);

HigherOrderGraph (k=2) with 863 nodes and 1886 edges
	Total edge weight = 1985.0
Edge attributes
	edge_weight		<class 'torch.Tensor'> -> torch.Size([1886])

Graph attributes
	num_nodes		<class 'int'>
	node_id		<class 'list'>

Spectral clustering with second-order graph Laplacian¶

In [55]:

#g2.to_undirected()
L = g2.get_laplacian(normalization='rw', edge_attr='edge_weight')

#g2_shuffled.to_undirected()
L_shuffled= g2_shuffled.get_laplacian(normalization='rw',edge_attr='edge_weight')

#g2.to_undirected() L = g2.get_laplacian(normalization='rw', edge_attr='edge_weight') #g2_shuffled.to_undirected() L_shuffled= g2_shuffled.get_laplacian(normalization='rw',edge_attr='edge_weight')

In [56]:

w,v = sp.linalg.eig(L.todense(),left= False, right = True)
w_shuffled, v_shuffled = sp.linalg.eig(L_shuffled.todense())

w,v = sp.linalg.eig(L.todense(),left= False, right = True) w_shuffled, v_shuffled = sp.linalg.eig(L_shuffled.todense())

In [57]:

fiedler = v[:,np.argsort(w)[1]]
fiedler_shuffled = v_shuffled[:,np.argsort(w_shuffled)[1]]

fiedler = v[:,np.argsort(w)[1]] fiedler_shuffled = v_shuffled[:,np.argsort(w_shuffled)[1]]

In [84]:

c=[]
a=[]
for v in g2.nodes:

    if int(v[0])<10 and int(v[1])<10:
        c.append('green')
        a.append(1)
    elif int(v[0])<20 and int(v[0])>= 10 and int(v[1])<20 and int(v[1])>=10: 
        c.append('red')
        a.append(1)
    elif int(v[0])<30 and int(v[0])>= 20 and int(v[1])<30 and int(v[1])>=20:
        c.append('blue')
        a.append(1)
    else:
        c.append('black')
        a.append(0.1)

c=[] a=[] for v in g2.nodes: if int(v[0])<10 and int(v[1])<10: c.append('green') a.append(1) elif int(v[0])<20 and int(v[0])>= 10 and int(v[1])<20 and int(v[1])>=10: c.append('red') a.append(1) elif int(v[0])<30 and int(v[0])>= 20 and int(v[1])<30 and int(v[1])>=20: c.append('blue') a.append(1) else: c.append('black') a.append(0.1)

In [88]:

c_shuffled=[]
a_shuffled=[]
for v in g2_shuffled.nodes: 

    if int(v[0])<10 and int(v[1])<10:
        c_shuffled.append('green')
        a_shuffled.append(1)
    elif int(v[0])<20 and int(v[0])>= 10 and int(v[1])<20 and int(v[1])>=10: 
        c_shuffled.append('red')
        a_shuffled.append(1)
    elif int(v[0])<30 and int(v[0])>= 20 and int(v[1])<30 and int(v[1])>=20:
        c_shuffled.append('blue')
        a_shuffled.append(1)
    else:
        c_shuffled.append('black')
        a_shuffled.append(0.1)

c_shuffled=[] a_shuffled=[] for v in g2_shuffled.nodes: if int(v[0])<10 and int(v[1])<10: c_shuffled.append('green') a_shuffled.append(1) elif int(v[0])<20 and int(v[0])>= 10 and int(v[1])<20 and int(v[1])>=10: c_shuffled.append('red') a_shuffled.append(1) elif int(v[0])<30 and int(v[0])>= 20 and int(v[1])<30 and int(v[1])>=20: c_shuffled.append('blue') a_shuffled.append(1) else: c_shuffled.append('black') a_shuffled.append(0.1)

In [83]:

plt.ylim(-.2, .25)
plt.scatter(range(g2.data.num_nodes), np.real(fiedler),c=c, alpha=a )

plt.ylim(-.2, .25) plt.scatter(range(g2.data.num_nodes), np.real(fiedler),c=c, alpha=a )

Out[83]:

<matplotlib.collections.PathCollection at 0x2c1211090>

In [87]:

plt.ylim(-.1, .1)
plt.scatter(range(g2_shuffled.data.num_nodes), fiedler_shuffled, c=c_shuffled, alpha=a_shuffled)

plt.ylim(-.1, .1) plt.scatter(range(g2_shuffled.data.num_nodes), fiedler_shuffled, c=c_shuffled, alpha=a_shuffled)

/Users/franziskaheeg/miniconda3/envs/pathpy3.10/lib/python3.10/site-packages/matplotlib/cbook.py:1699: ComplexWarning: Casting complex values to real discards the imaginary part
  return math.isfinite(val)
/Users/franziskaheeg/miniconda3/envs/pathpy3.10/lib/python3.10/site-packages/matplotlib/collections.py:194: ComplexWarning: Casting complex values to real discards the imaginary part
  offsets = np.asanyarray(offsets, float)

Out[87]:

<matplotlib.collections.PathCollection at 0x2c121b1f0>

Prepare the data¶

In [23]:

# Define edge indices for first and second-order graphs
edge_index_g1 = g.data.edge_index
edge_index_g2 = g2.data.edge_index

# Define edge indices for first and second-order graphs edge_index_g1 = g.data.edge_index edge_index_g2 = g2.data.edge_index

In [24]:

# Define edge weights
edge_weights = g.data['edge_weight']
edge_weights_higher_order = g2.data['edge_weight']

# Define edge weights edge_weights = g.data['edge_weight'] edge_weights_higher_order = g2.data['edge_weight']

In [25]:

# Define bipartite mapping
import torch

def generate_bipatite_edge_index(mapping = 'last'):

    if mapping == 'last':
        bipartide_edge_index = torch.tensor([list(g2.node_index_to_id.keys()),
                                     [i[1] for i in g2.node_index_to_id.values()]])

    elif mapping == 'first':
        bipartide_edge_index = torch.tensor([list(g2.node_index_to_id.keys()),
                                     [i[0] for i in g2.node_index_to_id.values()]])

    else:
        bipartide_edge_index = torch.tensor([list(g2.node_index_to_id.keys()) + list(g2.node_index_to_id.keys()),
                                     [i[0] for i in g2.node_index_to_id.values()] + [i[1] for i in g2.node_index_to_id.values()]])

    return bipartide_edge_index


# Original DBGNN implementation mapping = 'last'
bipatite_edge_index = generate_bipatite_edge_index(mapping='last')

# Define bipartite mapping import torch def generate_bipatite_edge_index(mapping = 'last'): if mapping == 'last': bipartide_edge_index = torch.tensor([list(g2.node_index_to_id.keys()), [i[1] for i in g2.node_index_to_id.values()]]) elif mapping == 'first': bipartide_edge_index = torch.tensor([list(g2.node_index_to_id.keys()), [i[0] for i in g2.node_index_to_id.values()]]) else: bipartide_edge_index = torch.tensor([list(g2.node_index_to_id.keys()) + list(g2.node_index_to_id.keys()), [i[0] for i in g2.node_index_to_id.values()] + [i[1] for i in g2.node_index_to_id.values()]]) return bipartide_edge_index # Original DBGNN implementation mapping = 'last' bipatite_edge_index = generate_bipatite_edge_index(mapping='last')

In [26]:

# Define the PyG data object
from torch_geometric.data import Data

num_nodes = max(max(g.data['edge_index'][0]), max(g.data['edge_index'][1])).item() + 1 # since indexing starts from 0
num_ho_nodes = max(max(g2.data['edge_index'][0]), max(g2.data['edge_index'][1])).item() + 1 # since indexing starts from 0

data = Data(
    num_nodes = num_nodes,
    num_ho_nodes = num_ho_nodes,
    x = torch.eye(num_nodes, num_nodes),
    x_h = torch.eye(num_ho_nodes, num_ho_nodes),
    edge_index = edge_index_g1,
    edge_index_higher_order = edge_index_g2,
    edge_weights = edge_weights.float(),
    edge_weights_higher_order = edge_weights_higher_order.float(),
    bipartite_edge_index = bipatite_edge_index,
    y = torch.tensor([ int(i) // 10 for i in paths.node_id])
)

# Define the PyG data object from torch_geometric.data import Data num_nodes = max(max(g.data['edge_index'][0]), max(g.data['edge_index'][1])).item() + 1 # since indexing starts from 0 num_ho_nodes = max(max(g2.data['edge_index'][0]), max(g2.data['edge_index'][1])).item() + 1 # since indexing starts from 0 data = Data( num_nodes = num_nodes, num_ho_nodes = num_ho_nodes, x = torch.eye(num_nodes, num_nodes), x_h = torch.eye(num_ho_nodes, num_ho_nodes), edge_index = edge_index_g1, edge_index_higher_order = edge_index_g2, edge_weights = edge_weights.float(), edge_weights_higher_order = edge_weights_higher_order.float(), bipartite_edge_index = bipatite_edge_index, y = torch.tensor([ int(i) // 10 for i in paths.node_id]) )

DBGNN¶

In [27]:

from sklearn.metrics import balanced_accuracy_score

def test(model, data):
    model.eval()

    _, pred = model(data).max(dim=1)

    metrics_train = balanced_accuracy_score(
        data.y[data.train_mask].cpu(),
        pred[data.train_mask].cpu().numpy()
        )

    metrics_test = balanced_accuracy_score(
        data.y[data.test_mask].cpu(),
        pred[data.test_mask].cpu().numpy()
        )

    return metrics_train, metrics_test

from sklearn.metrics import balanced_accuracy_score def test(model, data): model.eval() _, pred = model(data).max(dim=1) metrics_train = balanced_accuracy_score( data.y[data.train_mask].cpu(), pred[data.train_mask].cpu().numpy() ) metrics_test = balanced_accuracy_score( data.y[data.test_mask].cpu(), pred[data.test_mask].cpu().numpy() ) return metrics_train, metrics_test

In [28]:

data = RandomNodeSplit(num_val=0, num_test=0.3)(data)

model = DBGNN(
        num_features =[num_nodes, num_ho_nodes],
        num_classes = len(data.y.unique()),
        hidden_dims = [16, 32, 8],
        p_dropout = 0.4
        ).to(device)

optimizer = torch.optim.Adam(model.parameters(),  lr=0.005)
loss_function = torch.nn.CrossEntropyLoss()

data = data.to(device)

data = RandomNodeSplit(num_val=0, num_test=0.3)(data) model = DBGNN( num_features =[num_nodes, num_ho_nodes], num_classes = len(data.y.unique()), hidden_dims = [16, 32, 8], p_dropout = 0.4 ).to(device) optimizer = torch.optim.Adam(model.parameters(), lr=0.005) loss_function = torch.nn.CrossEntropyLoss() data = data.to(device)

In [29]:

data

data

Out[29]:

Data(x=[30, 30], edge_index=[2, 557], y=[30], num_nodes=30, num_ho_nodes=557, x_h=[557, 557], edge_index_higher_order=[2, 6572], edge_weights=[557], edge_weights_higher_order=[6572], bipartite_edge_index=[2, 557], train_mask=[30], val_mask=[30], test_mask=[30])

In [30]:

print(model)

print(model)

DBGNN(
  (higher_order_layers): ModuleList(
    (0): GCNConv(557, 16)
    (1): GCNConv(16, 32)
  )
  (first_order_layers): ModuleList(
    (0): GCNConv(30, 16)
    (1): GCNConv(16, 32)
  )
  (bipartite_layer): BipartiteGraphOperator()
  (lin): Linear(in_features=8, out_features=3, bias=True)
)

In [31]:

losses = []
for epoch in range(1000):
        output = model(data)
        loss = loss_function(output[data.train_mask], data.y[data.train_mask])
        loss.backward()
        optimizer.step()
        optimizer.zero_grad()
        losses.append(loss)

        if epoch % 10 == 0:
                train_ba, test_ba  = test(model, data)
                print(f'Epoch: {epoch}, Loss: {loss}, Train balanced accuracy: {train_ba}, Test balanced accuracy: {test_ba}')

losses = [] for epoch in range(1000): output = model(data) loss = loss_function(output[data.train_mask], data.y[data.train_mask]) loss.backward() optimizer.step() optimizer.zero_grad() losses.append(loss) if epoch % 10 == 0: train_ba, test_ba = test(model, data) print(f'Epoch: {epoch}, Loss: {loss}, Train balanced accuracy: {train_ba}, Test balanced accuracy: {test_ba}')

Epoch: 0, Loss: 1.227025032043457, Train balanced accuracy: 0.3333333333333333, Test balanced accuracy: 0.3333333333333333
Epoch: 10, Loss: 0.6666216850280762, Train balanced accuracy: 0.6666666666666666, Test balanced accuracy: 0.6666666666666666
Epoch: 20, Loss: 0.09434882551431656, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 30, Loss: 0.0014071125769987702, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 40, Loss: 0.00030880115809850395, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 50, Loss: 0.0001672431972110644, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 60, Loss: 0.00011002655082847923, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 70, Loss: 8.51466174935922e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 80, Loss: 7.0924885221757e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 90, Loss: 6.107875378802419e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 100, Loss: 5.376345507102087e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 110, Loss: 4.805967182619497e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 120, Loss: 4.343973705545068e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 130, Loss: 3.959159948863089e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 140, Loss: 3.632800871855579e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 150, Loss: 3.3529791835462674e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 160, Loss: 3.1117517210077494e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 170, Loss: 2.900604704336729e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 180, Loss: 2.7149984816787764e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 190, Loss: 2.5509601982776076e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 200, Loss: 2.4011105779209174e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 210, Loss: 2.2694241124554537e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 220, Loss: 2.1479540009750053e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 230, Loss: 2.0384035451570526e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 240, Loss: 1.9385019186302088e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 250, Loss: 1.8454114979249425e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 260, Loss: 1.7619706341065466e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 270, Loss: 1.6842053810250945e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 280, Loss: 1.6104137102956884e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 290, Loss: 1.5440009519807063e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 300, Loss: 1.47985856528976e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 310, Loss: 1.4213922440831084e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 320, Loss: 1.3663317076861858e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 330, Loss: 1.3135416338627692e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 340, Loss: 1.2641573448490817e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 350, Loss: 1.2193138900329359e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 360, Loss: 1.1761733730963897e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 370, Loss: 1.1353033187333494e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 380, Loss: 1.0955684956570622e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 390, Loss: 1.0592395483399741e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 400, Loss: 1.025181063596392e-05, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 410, Loss: 9.905548722599633e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 420, Loss: 9.610374036128633e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 430, Loss: 9.309522283729166e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 440, Loss: 9.031377885548864e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 450, Loss: 8.747555511945393e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 460, Loss: 8.480761607643217e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 470, Loss: 8.248027370427735e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 480, Loss: 8.026645446079783e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 490, Loss: 7.805261702742428e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 500, Loss: 7.583881142636528e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 510, Loss: 7.373850621661404e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 520, Loss: 7.19220361133921e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 530, Loss: 6.999202923907433e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 540, Loss: 6.823232070019003e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 550, Loss: 6.63590708427364e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 560, Loss: 6.471289452747442e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 570, Loss: 6.318023679341422e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 580, Loss: 6.164757451188052e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 590, Loss: 6.022844900144264e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 600, Loss: 5.8752552831720095e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 610, Loss: 5.756049631600035e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 620, Loss: 5.619813236990012e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 630, Loss: 5.506282832357101e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 640, Loss: 5.375722594180843e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 650, Loss: 5.2508389671857e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 660, Loss: 5.148661784915021e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 670, Loss: 5.035130925534759e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 680, Loss: 4.927277132082963e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 690, Loss: 4.8364522626798134e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 700, Loss: 4.745627848024014e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 710, Loss: 4.654803433368215e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 720, Loss: 4.563979018712416e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 730, Loss: 4.478830760490382e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 740, Loss: 4.399358658702113e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 750, Loss: 4.302858087612549e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 760, Loss: 4.2233859858242795e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 770, Loss: 4.14391388403601e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 780, Loss: 4.08147252528579e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 790, Loss: 4.007677034678636e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 800, Loss: 3.933881998818833e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 810, Loss: 3.871439730573911e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 820, Loss: 3.826027295872336e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 830, Loss: 3.7465554214577423e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 840, Loss: 3.6727599308505887e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 850, Loss: 3.621670884967898e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 860, Loss: 3.5649056826514425e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 870, Loss: 3.5138166367687518e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 880, Loss: 3.462727590886061e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 890, Loss: 3.4173153835581616e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 900, Loss: 3.3491965041321237e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 910, Loss: 3.303783614683198e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 920, Loss: 3.264047563789063e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 930, Loss: 3.2129585179063724e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 940, Loss: 3.1561926334688906e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 950, Loss: 3.1164572646957822e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 960, Loss: 3.054014541703509e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 970, Loss: 3.0199551019904902e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 980, Loss: 2.9688660561077995e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0
Epoch: 990, Loss: 2.9291297778399894e-06, Train balanced accuracy: 1.0, Test balanced accuracy: 1.0

Latent space representation of edges¶

In [32]:

g2.node_index_to_id[0]

g2.node_index_to_id[0]

Out[32]:

(0, 1)

In [33]:

model.eval()
latent = model.higher_order_layers[0].forward(data.x_h, data.edge_index_higher_order).detach()
node_embedding = TSNE(n_components=2, learning_rate='auto', init='random').fit_transform(latent.cpu())

colors = []
for v, w in g2.nodes:
    if data.y[v] == 0 and data.y[w] == 0:
        colors.append('red')
    elif data.y[v] == 1 and data.y[w] == 1:
        colors.append('green')
    elif data.y[v] == 2 and data.y[w] == 2:
        colors.append('blue')
    else:
        colors.append('grey')

plt.figure(figsize=(13,10))
plt.scatter(node_embedding[:,0], node_embedding[:,1], c=colors, alpha=0.5)

for e in g2.edges:
    s = g2.node_id_to_index[e[0]]
    t = g2.node_id_to_index[e[1]]
    plt.plot([node_embedding[s,0], node_embedding[t,0]], [node_embedding[s,1], node_embedding[t,1]], 
             color='lightsteelblue', 
             linestyle='-', 
             alpha=0.2,
             lw=0.2)
plt.axis('off')
plt.show()

model.eval() latent = model.higher_order_layers[0].forward(data.x_h, data.edge_index_higher_order).detach() node_embedding = TSNE(n_components=2, learning_rate='auto', init='random').fit_transform(latent.cpu()) colors = [] for v, w in g2.nodes: if data.y[v] == 0 and data.y[w] == 0: colors.append('red') elif data.y[v] == 1 and data.y[w] == 1: colors.append('green') elif data.y[v] == 2 and data.y[w] == 2: colors.append('blue') else: colors.append('grey') plt.figure(figsize=(13,10)) plt.scatter(node_embedding[:,0], node_embedding[:,1], c=colors, alpha=0.5) for e in g2.edges: s = g2.node_id_to_index[e[0]] t = g2.node_id_to_index[e[1]] plt.plot([node_embedding[s,0], node_embedding[t,0]], [node_embedding[s,1], node_embedding[t,1]], color='lightsteelblue', linestyle='-', alpha=0.2, lw=0.2) plt.axis('off') plt.show()

In [34]:

model.eval()
latent = model.higher_order_layers[1].forward(latent.cpu(), data.edge_index_higher_order).detach()
node_embedding = TSNE(n_components=2, learning_rate='auto', init='random').fit_transform(latent.cpu())

colors = []
for v, w in g2.nodes:
    if data.y[v] == 0 and data.y[w] == 0:
        colors.append('red')
    elif data.y[v] == 1 and data.y[w] == 1:
        colors.append('green')
    elif data.y[v] == 2 and data.y[w] == 2:
        colors.append('blue')
    else:
        colors.append('grey')

plt.figure(figsize=(13,10))
plt.scatter(node_embedding[:,0], node_embedding[:,1], c=colors, alpha=0.5)

for e in g2.edges:
    s = g2.node_id_to_index[e[0]]
    t = g2.node_id_to_index[e[1]]
    plt.plot([node_embedding[s,0], node_embedding[t,0]], [node_embedding[s,1], node_embedding[t,1]], 
             color='lightsteelblue', 
             linestyle='-', 
             alpha=0.2,
             lw=0.2)
plt.axis('off')
plt.show()

model.eval() latent = model.higher_order_layers[1].forward(latent.cpu(), data.edge_index_higher_order).detach() node_embedding = TSNE(n_components=2, learning_rate='auto', init='random').fit_transform(latent.cpu()) colors = [] for v, w in g2.nodes: if data.y[v] == 0 and data.y[w] == 0: colors.append('red') elif data.y[v] == 1 and data.y[w] == 1: colors.append('green') elif data.y[v] == 2 and data.y[w] == 2: colors.append('blue') else: colors.append('grey') plt.figure(figsize=(13,10)) plt.scatter(node_embedding[:,0], node_embedding[:,1], c=colors, alpha=0.5) for e in g2.edges: s = g2.node_id_to_index[e[0]] t = g2.node_id_to_index[e[1]] plt.plot([node_embedding[s,0], node_embedding[t,0]], [node_embedding[s,1], node_embedding[t,1]], color='lightsteelblue', linestyle='-', alpha=0.2, lw=0.2) plt.axis('off') plt.show()

Latent space representation of nodes¶

In [35]:

model.eval()
latent = model.forward(data).detach()
node_embedding = TSNE(n_components=2, learning_rate='auto', init='random', perplexity=10).fit_transform(latent.cpu())

colors = []
for v in g.nodes:
    if data.y[v] == 0:
        colors.append('red')
    elif data.y[v] == 1:
        colors.append('green')
    elif data.y[v] == 2:
        colors.append('blue')
    else:
        colors.append('grey')

plt.figure(figsize=(13,10))
plt.scatter(node_embedding[:,0], node_embedding[:,1], c=colors, alpha=0.5)

for e in g.edges:
    s = e[0]
    t = e[1]
    plt.plot([node_embedding[s,0], node_embedding[t,0]], [node_embedding[s,1], node_embedding[t,1]], 
             color='lightsteelblue', 
             linestyle='-', 
             alpha=0.2,
             lw=0.2)
plt.axis('off')
plt.show()

model.eval() latent = model.forward(data).detach() node_embedding = TSNE(n_components=2, learning_rate='auto', init='random', perplexity=10).fit_transform(latent.cpu()) colors = [] for v in g.nodes: if data.y[v] == 0: colors.append('red') elif data.y[v] == 1: colors.append('green') elif data.y[v] == 2: colors.append('blue') else: colors.append('grey') plt.figure(figsize=(13,10)) plt.scatter(node_embedding[:,0], node_embedding[:,1], c=colors, alpha=0.5) for e in g.edges: s = e[0] t = e[1] plt.plot([node_embedding[s,0], node_embedding[t,0]], [node_embedding[s,1], node_embedding[t,1]], color='lightsteelblue', linestyle='-', alpha=0.2, lw=0.2) plt.axis('off') plt.show()

In [ ]:

In [ ]: